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Fundamental Measurement of Force and Newton's First and Second Laws of Motion
David H. Krantz
Philosophy of Science
Vol. 40, No. 4 (Dec., 1973), pp. 481-495
Stable URL: http://www.jstor.org/stable/186283
Page Count: 15
You can always find the topics here!Topics: Axioms, Mathematical vectors, Vector spaces, Classical mechanics, Geometric shapes, Axiomatization, String, Kinematics, Coordinate systems, Mathematical theorems
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The measurement of force is based on a formal law of additivity, which characterizes the effects of two or more configurations on the equilibrium of a material point. The representing vectors (resultant forces) are additive over configurations. The existence of a tight interrelation between the force vector and the geometric space, in which motion is described, depends on observations of partial (directional) equilibria; an axiomatization of this interrelation yields a proof of part two of Newton's second law of motion. The present results (which were derived from a curious and deep isomorphism between force measurement and trichromatic color measurement) yield a kind of subunit, which needs to be incorporated into more complete axiomatizations of mechanics that would fulfill the Mach-Kirchhoff program.
Philosophy of Science © 1973 The University of Chicago Press